Check additivity vs multiplicativity of interventions

[adamkucharski]

In the odin implementation, we currently have multiplicative interventions on the contact rate, defined via a log transform:

  contact_reduction[, ] <- if (t > intervention_start[i] && t < intervention_end[i]) (1.0 - intervention_effect[i, j]) else 1 # nolint: line_length_linter.
  contact_reduction_log[, ] <- log(contact_reduction[i, j] + 1e-10) # Avoid zero
  contact_reduction_total_log[] <- sum(contact_reduction_log[, i])
  contact_reduction_total[] <- exp(contact_reduction_total_log[i])

This seems to matches the vignette output for overlapping interventions with the same parameter set.

However, the vignette states that "All further interventions are assumed to be additional percentage point increases on the effect of any active interventions.". This functionality comes from cumulative_contacts_intervention() in intervention.R. We should work out what's driving this difference.

[adamkucharski]

Update: the difference comes because the default scenarios for overlapping interventions in the vignette target different ages (children and adults), so the difference isn't obviously apparent. If instead we set the 1st intervention to c(0.3,0.3,0.3) and the second to c(0.7,0.7,0.7), we get non-zero transmission in the multiplicative odin assumption

and zero in the additive one:

This should be a reasonably straightfoward fix in the internal odin machinery – will flag on issue #254.

[adamkucharski]

Have pushed a fix to the odin model branch, and now get matching outputs for odin:

and original cpp: